C1 help please :)

Can someone please help me with this question? I've worked out part (a) and thought I'd worked out part (b) but when I substituted it into part (c), the answer was way off! :s-smilie:

The vertices of a triangle are A(2,4), B(-8,2) and C(4,-6).
The points P and Q are the midpoints of AB and AC respectively.
The line through P, perpendicular to AB, meets the line through Q, perpendicular to AC, at R.

a) Show that the equation on PR is y+5x+12=0 and find the equation QR

b) Find the coordinates of R

c) Show that BR=CR

For part (b), I 'found' the coordinates of R by solving the equations in part (a) simultaneously, as I could see from my sketch that the lines intersected one another, but I came out with R(0.4,-14), which I found out was wrong after using it to answer part (c) :frown:

Can anybody help me to work parts (b) and (c) out please?

Reply 1

jonny23563

12

Did you get QR right?

Reply 2

Zebra-Zahra

OP

jonny23563

Did you get QR right?

I'm not sure :s-smilie:

I got y-5x+16=0

Reply 3

mcp2

2

Find the gradient of the line of AB and do the same for AC and find the mid-points. Do you remember how to find the gradient of a line that's perpendicular to another? You were on the right track by using the simultaneous equations, just check your working out.

Reply 4

Zebra-Zahra

OP

mcp2

Find the gradient of the line of AB and do the same for AC and find the mid-points. Do you remember how to find the gradient of a line that's perpendicular to another? You were on the right track by using the simultaneous equations, just check your working out.

Ah, I've just realised that I worked one of the gradients out correctly, but wrote it down incorrectly, so that's why my answers don't make sense :smile:

Thank you for you help :smile:

C1 help please :)

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